Exploring the preservation of a parasitic trace in decapod crustaceans using finite elements analysis

The fossil record of parasitism is poorly understood, due largely to the scarcity of strong fossil evidence of parasites. Understanding the preservation potential for fossil parasitic evidence is critical to contextualizing the fossil record of parasitism. Here, we present the first use of X-ray computed tomography (CT) scanning and finite elements analysis (FEA) to analyze the impact of a parasite-induced fossil trace on host preservation. Four fossil and three modern decapod crustacean specimens with branchial swellings attributed to an epicaridean isopod parasite were CT scanned and examined with FEA to assess differences in the magnitude and distribution of stress between normal and swollen branchial chambers. The results of the FEA show highly localized stress peaks in reaction to point forces, with higher peak stress on the swollen branchial chamber for nearly all specimens and different forces applied, suggesting a possible shape-related decrease in the preservation potential of these parasitic swellings. Broader application of these methods as well as advances in the application of 3D data analysis in paleontology are critical to understanding the fossil record of parasitism and other poorly represented fossil groups.


Introduction
Parasitism is the most common and ecologically impactful mode of life today, as parasitic taxa comprise at least 40% of described extant species and are critical to ecosystem trophic structure [1].However, evidence of parasitic behavior in the fossil record is uncommon [2].
Studies describing cases of potential fossil evidence of parasites span several decades [3][4][5], but broader synthesis and interpretation of fossil parasitic evidence has only recently been undertaken because of broader data access, an increase in studies, and computationally intensive tools [6].Despite these advances, existing evidence and data of fossil parasitism is limited, taxonomically biased, and often over-represented by sites of exceptional preservation.
Taphonomic bias is suggested to be a main factor causing these disparities because many ubiquitous modern parasitic taxa are soft-bodied, small, and/or endoparasitic, with little chance of producing recognizable fossil evidence [7][8].Many modern marine parasites create distinct traces on their host's skeletal elements, yet, for many taxa, fossil evidence of these parasites and traces is uncommon.Biases against evidence of parasitism in the fossil record have largely yet to be critically examined or quantified [9][10][11][12][13].As a result of the scarcity of parasitic evidence, the fossil record of parasitism remains a major gap in the scientific understanding of the evolutionary and ecological history of life on earth.Crustaceans are a highly diverse, abundant, and globally distributed group of arthropods, with a fossil record spanning more than 500 million years.Crustaceans are well documented as a group in which many novel parasitic interactions have arisen independently several times, with crustaceans exhibiting great diversity as both hosts and parasites [12].Some of the parasitic relationships among crustaceans produce distinct, preservable traces, that can be identified from fossil host specimens [12].These features make crustaceans an excellent model group for studying the fossil record of parasitism.The fossil record of crustaceans is limited, and often fragmentary, owing to a lightly to moderately (and often heterogeneously) calcified exoskeleton that readily disarticulates in the absence of soft tissue [14].Many crustaceans are found in concretions, typically calcite or siderite, which preserve high fidelity 3D fossils, sometimes with original exoskeletal material remaining [15][16][17].Fossiliferous concretions are a unique and exceptional taphonomic scenario, suggesting rapid burial and rapid microbially and geochemically mediated concretionary growth of carbonate minerals, which only occurs under specific conditions [18].Crustaceans have also been the subject of taphonomic study, revealing the fragmentary and biased nature of the crustacean fossil record, controlled largely by differences in calcification across individuals and between taxa and depositional conditions [9,14,19].
Extant crustacean hosts and their parasites are the subject of much study, as a result of being relatively ubiquitous in marine ecosystems, as well as their significant economic and ecological importance, but fossil evidence of parasitism among crustaceans is limited [12].
Suboval branchial swellings found on decapod carapace fossils, identified as the ichnotaxon Kanthyloma crusta [11], are among the most well understood examples of fossil parasitism of crustaceans.These traces are inferred to be induced by parasitic epicaridean isopods that commonly produce identical traces on modern decapods [11].These distinct fossil swellings have been found on diverse decapod fossils since an early peak in the number of parasitized host species in the Late Jurassic, found predominantly in Europe [20].Likely using the Tethys as a dispersal pathway, K. crusta has been observed on decapod fossils globally through the Cretaceous and Cenozoic, although with lower host diversity than seen in the Late Jurassic [21].
Extant isopods in the family Bopyridae, which induce branchial swellings attributable to K. crusta, are globally widespread and infest diverse decapod species [22], in contrast to the relatively poor Cenozoic fossil record of K. crusta.Modern bopyrid isopods are widespread parasites of decapods, typically at relatively low prevalence (<5%) within host populations, but can instigate rapid host population collapse when introduced to a naïve host population [13,23].
As high-quality specimens of fossil decapods are rare and scientifically valuable, particularly those bearing additional abnormalities such as traces of parasitism, destructive sampling techniques and intrusive attempts to reveal fossils from the matrix are inadvisable.CT scanning has seen a dramatic increase in widespread use for paleontological study over the last 20 years, as the technology has become more accessible, and CT data has become easier to analyze and manipulate [24][25][26][27][28][29][30].
Computational simulation techniques, such as finite element methods and computational fluid dynamics, have been used to simulate physical forces acting on 3D models to explore functional morphology and ecology in fossils [31][32].Studies over the last two decades have applied finite elements analysis (FEA) to paleontological and zoological material, including morphological study of fossil arthropods and modern crustaceans [32][33], and found that highfidelity finite-element models of living and fossil organisms are robust at modelling strain and resolving relationships between form and function [34][35][36].
The aim of this study is to present the first application of FEA in evaluating the impact of the parasite-induced trace fossil Kanthyloma crusta on host preservation by exploring how deformations of carapace shape alter the physical preservation potential of the host.Specimens of modern and fossil decapod crustaceans with branchial swellings attributed to isopod infestation (K.crusta) were CT-scanned, and FEA was conducted to observe differences in the magnitude and distribution of stress on healthy and swollen branchial chambers.

Specimens studied
Seven specimens of recent and fossil decapod specimens with swellings attributable to K. crusta were studied through institutional loans: three Recent specimens of Munida valida [37] from the Gulf of Mexico preserved in 70% ethanol (Fig

Scanning and CT data preparation
X-ray computed tomography (CT) is a technology that uses an X-ray source to construct several cross-section radiographs, which can then be combined to form a 3D volumetric render of the scanned subject [24].Specimen 3D data for analysis was captured using a North Star Imaging (NSI) X3000 industrial CT x-ray inspection system.All CT scans were conducted at sub-35μm resolution.Simultaneous CT scans of multiple specimens (including the Munida and Macroacaena specimens) utilized the NSI SubpiX [40] scanning technique for increased resolution.CT data was initially processed and visualized using the NSI efX software and was then exported as TIFF images stacks for further preparation.The image stacks output was imported into the software Dragonfly ORS 2022.1 [41] for visualization and 3D conversion of the CT data.The specimens were segmented from the raw data using a mixture of manual segmentation and manually trained AI-assisted segmentation models [41].Segmented specimen data was rendered for visualization in Dragonfly, then exported as Stereolithography (STL) 3D models.Specimen STLs were imported into the software Blender 3.4 [42] for additional cleaning and processing, including removal of unconnected elements, remeshing, downscaling, and fixing geometry errors.After cleaning and fixing errors, each model was standardized to a uniform size and to a uniform number of faces (20,000±1,000) to improve comparability of results between specimens.

Finite elements analysis
Finite elements analysis (FEA) is a simplified method of testing the load and distribution of physical stresses on a complex 3D model with given material properties, forces, and constraints, by subdividing a complex model into finite parts, then solving partial differential equations for the parts individually [43].The prepared specimen 3D models were imported into the software FreeCAD 0.20.2[44] and converted into FEA models using the program Gmsh 4.11.1 [45].In FreeCAD, identical material properties were applied to each model, which were amalgamated from multiple studies of the material properties of decapod skeletal elements [46][47][48][49][50].The ventral surfaces of the specimens were set as constraints, and a force of ten newtons of point load force was applied at perpendicular angles to faces at the same location on both the left and right branchial chamber of each specimen (for each specimen, this included one normal branchial chamber and one swollen branchial chamber) (Fig 2).All FEA was also run using applied forces of five newtons and twenty newtons, to assess results sensitivity.Swanson et al.
(2013) [51] demonstrated that ten newtons may be sufficient to indent or fracture a crustacean carapace of similar sizes to the specimens included here.Blue crabs, common scavengers and predators of small crustaceans along the east coast of the Americas, have been shown to exert point load forces in excess of 10 newtons at the tip of the dactyl in vivo [52][53].The finite elements analysis was solved using the solver CalculiX 2.10 [54], then the results were exported into Paraview 5.11.0 [55] as Visualization Toolkit (VTK) files for observation and visualization of FEA results.Von Mises stress, the stress response of a given material relative to the limit at which the material deforms, was chosen as the primary FEA output metric for characterizing the stress, strain, and deformation of the models in response to a force [56].The vertex data from the left and right side of each mesh were isolated from each other to compare von Mises stress values between the normal and swollen side of each specimen.

Computed Tomography
Specimen CT scans output high-resolution 3D data, with a voxel size of 30.

Finite Elements Analysis
The finite elements analysis output meshes comprised of tens of thousands of vertices which store individual stress, strain, and deformation values.The stress was highly localized to the area immediately around the site of applied force in all models and was not distributed to other areas of the branchial chamber or carapace (Fig 4).The peak stress on the swollen chamber was higher than on the healthy chamber for all specimens, although the magnitude of the difference varied considerably between specimens, from a 1.53% difference in the specimen of P. nanus, to a 51.00% difference in M. valida specimen A, with a mean of a 24.13% difference in peak stress, and median of 20.54% peak stress across all specimens (Figs 4 and 5, Table 1).
When considering high-stress values directly at the site of the applied force (Fig 5), there are minimal differences in distribution between the normal and swollen sides of each specimen, although the broader trend of highly localized stress peaks, resulting in right-skewed distributions, is observed in most specimens even when excluding smaller stress values.These distributions of stress and differences in peak stress are insensitive to changes in input force, except for the specimen of P. nanus, which had peak stress vary between the swollen and healthy chamber at different input forces but maintained peak stress differences below 2% (tested at 5N and 20N, S1 and S2 Figs, S1 Table ).FEA results stress values are stored and accessible through the repository Dryad [57].All stress values are in megapascals (MPa).

Discussion
The results of the finite elements analysis for the seven specimens are indicative of higher overall stress at a swollen branchial chamber relative to a healthy branchial chamber resulting from the same force.Four of the specimens have greater overall mean stress on the swollen chamber relative to the healthy chamber, and all specimens except for the M. rosenkrantzi specimen C have greater median stress on the swollen chamber, although due to the highly localized nature of each models' stress response (Fig 4), and the greater number of vertices on a swollen branchial region resulting from the shape deformity relative to a normal branchial region, means and medians of stress values are not directly comparable.When the results include only the vertices with high stress values around the site of the applied force (above 5 MPa: Fig 5 and Table 1), the number of vertices is similar between healthy and swollen chambers, four of the specimens have greater median stress on the swollen chamber, and the mean stress is higher on the swollen chamber for all but the specimen of P. nanus.These patterns, as well as the overall distribution of stress and differences in peak stress, are insensitive to changes in the magnitude of applied force, although the peak stress on the specimen of P. nanus varied between the healthy and swollen chamber at different forces while maintaining a peak difference below 2% (S1 and S2 Figs, S1 Table ).This difference in P. nanus, in combination with the small difference in peak stress between normal and swollen regions and greater variability of results Fossil preservation is a complex combination of biological, ecological, and environmental factors and conditions which are not fully explored here.Although point load forces as used in this analysis can be applied by some common crustacean scavengers and predators [52][53], point load forces do not represent the full range of forces and pressures that decapod skeletal material may be subjected to before burial.Decapods exhibit considerable differences in shape, cuticle thickness, and calcification between species, as well as ecological differences between taxa which have considerable taphonomic impacts [14].In addition, the presence of soft tissue and reabsorption of calcium before molting may result in considerable differences in preservation between corpses and molts [64].Each of these factors must be examined together going forward to understand the diverse preservation characteristics of crustaceans and their parasites through time, and subsequently crustacean parasite-host dynamics throughout earth's history.In this study of seven specimens across three species, the changes to body shape induced by a crustacean parasite swelling and their impact on preservation were isolated from the many other factors affecting preservation.Thus, there is considerable work still to be done, both in understanding the relationship between shape and preservation in these fossil parasite traces, and in contextualizing the preservation of the fossil record of crustacean parasites more broadly.The methods presented here must be further refined and broadly applied to better characterize the preservation of parasites in the marine fossil record.The complexity of preservation necessitates future refinements to the FEA methods used here, which should strive to incorporate increased model resolution, improved fidelity of material properties, and implementation of carapace thickness, as well as implementing advances to the fidelity and application of FEA in paleontology such as non-linearities [65].The significant differences between species and individuals also emphasize the importance of investigating patterns of parasite host-preservation with larger numbers of fossil and modern specimens, and across larger numbers of species.These computationally intensive scanning and analytical methods are especially valuable non-destructive tools for in-depth study of rare fossil occurrences, such as parasitic traces, but it is also critical to ground truth these results through experimentation with modern proxies, as well as thorough study of institutional fossil collections.All stress values are in Megapascals (MPa).

Fig 1 .
Fig 1. Specimens with branchial swellings.All scale bars are 1cm.Red arrows indicate

Fig 2 .
Fig 2. Finite Element Model of Macroacaena rosenkrantzi with constraints in FreeCAD.Red 5 microns for the specimen of P. nanus, and a voxel size of 26.4 microns for the Munida valida and Macroacaena rosenkrantzi specimens (Fig 3 A-G).The higher resolution of the Munida and Macroacaena specimens is a result of the SubpiX scanning technique.CT data of the recent Munida specimens revealed complex internal morphology and considerable heterogeneity of cuticle density and thickness (Fig 3 A-C).The scans of the fossil Macroacaena in concretions had no recognizable internal morphology, or internal evidence of the isopod parasite, although some of the original host cuticle was intact and is distinguishable from the concretion (Fig 3 D-F).The Panopeus specimen CT data revealed that it is an isolated carapace, possibly a molt, with no preserved cuticle, and that the swollen right side of the carapace is filled with limestone material, while the normal left side of the carapace contains a large void (Fig 3 G).

Fig 3 .
Fig 3. CT data of specimens.All specimens are shown in transverse cross-section.Scale bars

Fig 4 .
Fig 4. FEA results meshes.Swellings are displayed to the right and circled in red for each

Fig 5 .
Fig 5. Histograms of model vertex von Mises stress values exceeding 5 MPa.Red lines under different forces, is likely a reflection of the considerably different body plan of Panopeus relative to Munida and Macroacaena.The relatively elongated and rounded body plans of Munida and Macroacaena resulted in laterally exaggerated branchial swellings relative to the flat and wide body plan of Panopeus, which has the least visually apparent swelling of the specimens studied.This difference may reflect broader differences in the impact of K. crusta on preservation across decapod taxa and body plans.The observed trend, with greater peak stress in response to the same force at the site of a parasite-induced branchial swelling relative to a normal branchial chamber for each specimen, may represent an early indication of a shape-related decrease in fossil preservation potential for Kanthyloma crusta.If correct, a taphonomic bias against the preservation of this parasitic trace implies reduced fossil prevalence and host diversity relative to the fossil record of unparasitized hosts.These results emphasize the importance of recontextualizing the fossil record of K. crusta and parasitism more broadly to disentangle fossil record and sampling biases from true signals in the fossil record of parasitism.Non-destructive, computationally intensive methods, as presented here, are key to revealing ecological and evolutionary trends in the fossil record of parasitism.Resolving this gap is crucial as it has become imperative to understand and predict how a changing climate will impact parasite-host dynamics.Studies predicting changes in parasite-host dynamics relating to anthropogenic change have produced varying results, owing to geographic and taxonomic unevenness of climate change impacts.However, it appears likely that climate change will induce shifts in the range, prevalence, and diversity of parasites, leading to widespread consequences for global ecosystems[58][59][60][61][62].It is crucial to constrain the fossil record of parasite evolution and ecology to better create a baseline for the impacts of anthropogenic change, as well as to model the consequences of climate change on parasites from comparable climate events in the fossil record, such as the Paleocene-Eocene Thermal Maximum[63].

Table 1 . Summary of von Mises stress values from specimen FEA
the University of Florida, Florida Museum of Natural History, Invertebrate Paleontology; Laura Cotton, Arden Bashforth, and the Natural History Museum of Denmark.(Reviewers…)